Poisson approximation to a Binomial distribution . The Poisson distribution is often used as an approximation to the Binomial distribution for large n and small p, as the Poisson probabilities are easier to calculate.
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The Poisson approximation to a Binomial distribution may be made provided n is large. In addition p must be quite small, otherwise the two distributions would not exhibit similar amounts of positive skew.
X ~ Bin(n, p) approximated by
Po(np) where = np.
: = np = 250 0.015 = 3.75
(a)P(X = 0) = e-3.75= 0.0235
P(X ≥ 2) = 1 – [P(X=0)+P(X=1)]
= 1 – [0.0235 + e-3.75 3.75 ] = 0.888
Ans3: = np = 180 1/36 = 5(a)P(X=1) = e-5 5 = 0.0337 (b) P(X=2) = e-525/2 = 0.0842(c) P(x ≥ 3 ) = 1 – P(X ≤ 2 ) = 1 – 0.1247 = 0.8753= 0.875 (3sf)Go back